This is really just an extended comment on CuriousOne's answer.
You probably know that there are just a few elementary particles: six quarks, three electron-a-likes (electron, mu and tau), three neutrinos and various assorted bosons. All matter is made up from various combinations of these particles.
The problem is that the heavy particles decay into the light ones on short timescales. So top, bottom, charm and strange quarks end up as up and/or down quarks while tau and mu end up as electrons. So very quickly everything ends up as electrons and up and down quarks, which of course make protons and neutrons.
The energy difference between up and down quarks is relatively small, and indeed it's comparable to nuclear binding energies. That's why a neutron can be stable in a nucleus and unstable out of it, because the nuclear binding energy is large enough to stabilise the neutron. However in all other cases the energy difference between the different types of quarks is far larger than nuclear energies and (apart from some special cases - see below) there is no stabilising them. Likewise the energy differences between the electron, mu and tau are too large for the heavier particles to be stabilised by atomic binding energies.
I've skipped over the bosons because you can't make matter from bosons. Bosons don't obey the Pauli exclusion principle, and it's the exclusion principle that allows atoms to exist. If you attempted to make matter from bosons at best you just get a condensate.
I did say there we some special cases. Let me start with a known one: you can make matter from muons. Muonic hydrogen has been made, and so has a hydrogen analogue made from an anti-mu and electron. I thought the mu/anti-mu equivalent of hydrogen had been observed, but Wikipedia says not. Anyhow, these atoms last only until the mu decays. As mentioned above, the binding energies available are too small to stabilise the mu and prevent it decaying to an electron.
The other special case is still entirely theoretical. A neutron is stable because the nuclear binding energy is high enough to prevent the down quark to up quark decay, but nuclear energies aren't high enough to prevent for example a strange quark decaying. However it has been suggested that at exceedingly high pressures the strange quarks could be stabilised and form strange matter. Most of us regard these ideas as huge fun but rather unlikely.